1.

`(dy)/(dx)` ज्ञात कीजिए : `y=tan^(-1)((3x-x^(3))/(1-3x^(2))),-(1)/(sqrt3)lt x lt (1)/(sqrt3)`

Answer» `y=tan^(-1)((3x-x^(3))/(1-3x^(2)))" "{:("माना "x=tan theta),(rArr theta= tan^(-1)x):}`
`rArr" "y=tan^(-1)((3 tan theta- tan^(3) theta)/(1-3 tan^(2) theta))`
`=tan^(-1)(tan 3 theta)=3 theta = 3 tan^(-1)x`
`rArr" "(dy)/(dx)=3(d)/(dx) tan^(-1)x=(3)/(1+x^(2))`


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